There are a few significant antenna system designs that may sometimes call for a serial connection of feedlines, as well as a further serial connection to a source. Radio amateurs especially do not think about this possibility when designing antenna systems, since the parallel connection is so ingrained into their thinking. Therefore, let's examine a few cases in which a serial connection of multiple feedlines is a plausible way to proceed and then develop some easy methods of modeling the situation within NEC.

**Junctions of 2 Identical Feedlines**

There are a number of simple 2-element phased
arrays that have been available to designers for about 3/4 of a
century. The designs are straightforward and reliable. Interestingly,
in the past, we have used a parallel connection of the identical
feedlines from each element to a center point that is also the main
feedpoint for the array. **Fig. 1** shows one such array, the
venerable W8JK.

The W8JK is a flattop or endfire array with its bi-directional main lobes off the end of the plane formed by the two wires. There are many version of the W8JK, with various element lengths and element spacing values. In general, the longer that we make the elements, the higher will be the gain of the array--up to an element length of about 1.25 wavelengths. As well, the closer that we space the elements, the higher will be the array gain, with the penalty that the impedance at the junction of the two phasing feedlines tends to decrease as the spacing decreases.

Properly phasing the two elements means feeding one element 180 degrees out of phase with the other element. If we use identical lengths of identical feedlines for the phasing lines, then giving one and only one of the lines a half twist will effect the desired phasing.

Most implementations of the W8JK array employ one of the common parallel feedlines. For our sample, we shall employ 600-Ohm open ladder line, since it has lower losses than 450-Ohm window line or 300-Ohm tubular transmitting line. The latter two have vinyl casings that provide structural integrity for the line, but those casings increase losses relative to the ladder line that uses only periodic spacers to maintain the distance between the two wires forming the feedline. Note that the 300-Ohm line specified is a version designed for transmitting applications. The typical TV twinlead, especially the cheaper varieties, may have much higher losses and, indeed, may not have a 300-Ohm characteristic impedance.

In our example, let's also use the same 600-Ohm line as the main feedline. For many phased array installations, the length of feedline from the antenna system feedpoint junction to the equipment can be very long. Let's specify 100', although real installations may be much longer.

One of the dangerous sound-bite ideas that
pervades amateur radio practice is that the losses in a parallel
feedline are so low that its length and the SWR mismatch between the
line's characteristic impedance and the antenna terminal impedance do
not matter. The line will provide a high-efficiency power transfer from
the equipment to the antenna system (or vice versa on receive)
regardless of the line length or the mismatch. Unfortunately, this
sound bite is only correct up to a point. Like any feedline, even the
600-Ohm open ladder line has a baseline matched loss value per unit of
length. A mismatch creates additional loss such that the SWR acts as a
multiplier on the matched loss value. The higher the SWR value, based
on the mismatch between the line characteristic impedance and the
antenna terminal impedance, the greater will be the losses on the line.
**Table 1** provides some approximate values of loss in 600-Ohm open
ladder line for 100' of the line at two frequencies--14.175 and 28.5
MHz in the sample--to show the rising losses as the SWR increases.

The values are approximate because we can find slightly different values in different tables of matched loss values, as well as slightly different values for the characteristic impedance of the line. In addition, we would discover different loss values depending on whether the mismatch is due to very high or very low antenna terminal impedance values. However, the values shown are useful as approximations. You may explore AC6LA's TLD program or N6BV's TLW program for more refined figures for different line lengths, different antenna terminal impedance values, and different lines. The numbers in the chart derive from using purely resistive impedances.

The baseline losses of 450-Ohm and 300-Ohm lines are considerably higher, relative to the 600-Ohm line shown. Hence, with very high SWR values, the overall loss for 100' of line will be proportionally higher. An SWR value of 32:1 is unusual, to say the least, if we think of impedances above 600 Ohms. A resistive impedance of 19,200 Ohms will yield the value. However, the much more commonly encountered value of 18.75 Ohms will also yield the same SWR value. The calculation of SWR from the antenna terminal impedance and the line characteristic impedance falls outside the scope of these notes, but the reactive component of the impedance is not a small factor in the calculation. Hence, in practical situations, SWR values above 10:1 are very common and values above 20:1 are not unusual.

Now let's add a further premise to our exercise: we wish to minimize so far as possible losses along the main 600-Ohm feedline from the antenna system terminals to the equipment. The next question is what this might mean for our W8JK monoband flattop. Let's construct one in model form using 1-wavelength elements spaced 1/2-wavelength apart at 21.225 MHz. Further, let's place the model 1 wavelength above average ground. Initially, let's use two phase lines, each with its own source. We can give one of the phase lines a half twist by specifying that it is reversed or we can leave both lines normal and set one of the sources at a 180-degree phase angle. If we exercise either option, we obtain a pair of source impedance values that read close to 84 + j88 Ohms.

If we construct the W8JK using the standard
parallel connection of the feedlines, then the impedance at the system
terminals at the source applied to the wire forming the junction of
phase lines becomes about 42 + j44 Ohms. Of course, we might add series
capacitance to the line and employ a 50-Ohm coaxial cable as the main
feedline, but that exercise belongs to a different discussion. We are
committed to using 600-Ohm ladder line as our main feedline. However,
as shown in **Table 2**, the 600-Ohm SWR is above 14:1.

One much neglected method of reducing the SWR on
the main feedline is to use a series connection at the main junction of
phasing and feedlines. **Fig. 2** shows the difference in the
connection in schematic form. The "+" and "-" signs are simply
reference points to keep the connections correct. Since most
installations would use some sort of fixture--perhaps a simple plate
that provides terminals and strain relief for the lines--one method is
no harder to implement than the other.

The last line in **Table 2** shows what we
gain from using a serial connection. The 600-Ohm SWR is under 4:1. The
voltage and current excursions along the main feedline will be much
lower than with the parallel connection. A concomitant result is that
the range of potential impedance values that the antenna tuner might
encounter will be smaller than with the parallel connection. Let's
assume that this condition is desirable and so we opt for the serial
connection.

Modeling the serial connection requires us to
rethink the requirements. A parallel connection only needed one very
short, very thin wire at the junction of the TL-based transmission
lines, and this same wire served as the source wire segment as well.
However, we need a different scheme for the serial connection. **Fig.
3** shows a usable method for two-line serial junctions with a
source.

The triangle consists of three very short and very thin wires. In the HF region, I typically use AWG #20 wire (0.032" diameter). The segment lengths are between 0.0015 and 0.002 wavelengths long, to keep the segment length within NEC limits. The very small triangle can go between the elements without harm. However, you can also specify a considerable distance away from the main radiating elements, since the transmission-lines, using the TL facility, have lengths specified by the command and not by the geometric distance between the elements and the junction assembly.

In all cases, the modeler should check the average gain test (AGT) for the array plus the serial assembly to ensure an adequate value for accuracy. The gain of the array should not change more than about 0.01 dB between the parallel and the serial models--or between either one and the model using separate sources, assuming that there is no difference in the specified transmission lines for the model set. In the figure, one dashed line is the "normal" line to one element, while the other dashed line is the "reversed" line to the second element. The source assembly is not totally invisible to the model, since the impedance values among the three models in the set will not show mathematical perfection to the last decimal place. Nonetheless, the models are good indicators of the anticipated performance, and construction variables will in most cases outweigh the slight differences in the calculated impedance values.

Serial feeding is not a solution to all
conditions associated with W8JK feedline junction values. Let's briefly
consider a flattop array consisting of two 44' elements with a 22'
spacing between them. The element length is about 1.25-wavelengths at
10 meters. As we reduce the operating frequency, the elements grow
shorter when measured in wavelengths, but so too does the element
spacing. As a consequence, the array provides relatively consistent
gain performance from 10 meters down to 30 meters. **Table 3**
shows the free-space performance modeled for such an array using AWG
#12 copper wire. As in the initial model, the phase lines
are 600-Ohm open ladder line, as is the presumed main feedline.

As the elements grow shorter while we reduce the operating frequency, the beamwidth grows wider. However, the maximum bi-directional gain remains relatively constant, varying by only 0.6 dB from one end of the operating spectrum to the other. The remaining columns show the feedpoint junction impedance with both parallel and serial feed systems, along with the 600-Ohm SWR as an indicator of probable losses along the main feedline. From 20 through 10 meters, the parallel feed system shows a maximum SWR value of nearly 15:1 at 15 meters, but the other values are lower, with the best values at 10 and 20 meters. However, the SWR value at 30 meters is above 40:1, a condition that promises possibly significant loss and very wide swings of voltage, current, and impedance along the main feedline. In contrast, the series feed system reduces the 30-meter SWR value almost by half, but ends up with higher SWR values on 10 and 20 meters. If we exclude a remote switching system at the main feedline junction with the phasing lines, the potential user is faced with a decision on which feeding system to use based upon which bands are more important to the station's operating goals.

A second type of array suitable for potential
serial feeding is the lazy-H, a broadside array consisting of two
elements that are vertically arranged and that provide a bi-directional
broadside pattern. **Fig. 4** provides a sketch of a monoband
version of the antenna using 1-wavelength elements and a spacing of
1/2-wavelength between the elements. For our sample, the midpoint
between the elements, where the phasing lines join, is 1 wavelength
above average ground. The difference between the lazy-H and the W8JK--a
difference that is crucial to operation--lies in the phasing system.
The vertically aligned lazy-H elements are fed in phase.

Although different in their exact values, the
impedance values at the lazy-H feedline junction are similar to those
of the W8JK. **Table 4** lists the impedance values for separately
sourced phase lines, for a parallel combination, and for a serial
combination. The performance of the array is almost incidental to our
purpose in using it, but the lazy-H does show about 1.5-dB higher gain
than the same wires and spacing applied to the W8JK, largely as a
function of a reduction in the strength of the higher-angle elevation
lobes. The TO angle is a degree lower than provided by the W8JK because
the effective height of the lazy-H is a small distance above the center
point between elements.

Since the lazy-H individual source impedance
values are lower than the corresponding W8JK values, the parallel
feedpoint system results in a higher 600-Ohm SWR value. The serial feed
system creates an SWR values that promises lower losses and narrower
impedance excursions along the main feedline, which may result in an
easier tuning task, depending upon the exact line length. The serial
system for modeling can use the same triangle of short, thin wires used
for the W8JK--either centered or at a large distance from the main
radiating elements. The only modeling difference related to the phase
lines is that both must be either "normal" or "reversed." Nevertheless,
the physical implementation of a serial feedline system will have a
quite different appearance, as suggested by the schematic outline in **Fig.
5**.

Unlike the W8JK, the lazy-H radiation properties
are not constant as we reduce the operating frequency. Shorter elements
and reduced element spacing both reduce gain in the lazy-H, since we
are feeding the elements in phase. Consider a pair of 44' lazy-H
elements spaced 22' apart vertically in free space. The elements are
about 1.25-wavelengths long on 10 meters, with a spacing of about
5/8-wavelength. These conditions optimize gain on 10 meters. On all
lower bands, the shorter elements and decreased spacing--as a function
of a wavelength--decrease gain. As well, they increase the beamwidth at
a faster rate than we saw in the comparable data for the W8JK. **Table
5** shows the data for all bands from 10 down to 30 meters using
series and parallel feed systems.

The gain of the lazy-H at 30 meters is marginal in the sense of being less than one dB higher than for a single-wire dipole. However, the array is usable if we can obtain satisfactory feedpoint junction impedance values. With a parallel connection, we find numerous bands with 600-Ohm SWR values above 10:1. Using a series connection, all but one of the bands shows a 600-Ohm SWR value of less than 10:1. However, the single band with a higher value is 10 meters, where the SWR value is very much higher and the losses for any given SWR value are the highest among all of the bands. Like the W8JK, the decision whether to use a parallel or a series connection does not make itself.

We have used very specific examples of both the W8JK and the lazy-H array in providing examples of the required modeling for effective evaluation. One may change the transmission line, the phase line, and even the length of the phase lines in search of a better combination using either serial or parallel feeding. With a central feedpoint between the elements, the only requirement (besides the W8JK half twist) is that both phase line be identical, including length. However, there is in principle no restriction on the length of the phasing lines. Therefore, one may search for lengths that provide the lowest SWR values relative to the desired main feedline for the bands of highest interest. All of this, of course, rests on the initial premise that one of our goals is to reduce main line losses to a minimum and, almost incidentally, to provide the antenna tuner with the least extreme resistance or reactance conditions at the terminals.

**A Three-Line Serial Feeding Example**

Serial feeding is also possible with more than
two lines that meet at a junction. Consider a triangle of three dipoles
for 2 meters. **Fig. 6** shows some of the details of a prototype
modeled and built for an article in *QST*. The elements are 1/2"
diameter aluminum on a PVC structure for support. The arm length, the
element length, and the spacing between dipole tips are all selected to
provide a horizontally polarized omni-directional pattern. The design
case used the band center as the design frequency, because the pattern
does not change within the confines of 2 meters and the SWR remains low
at the final junction with the 50-Ohm main feedline.

The design is predicated on the fact that a triangle of dipoles, properly spaced, yields the desired omni-directional pattern within perhaps 0.3 dB total variation. As detailed in other documents, the principles of operation differ from the 1961 Big Wheel arrangement. The older antenna creates a circular element with three high impedance feedpoints. Parallel lines from the feedpoints effect in the 1/4-wavelength distance to the hub an impedance transformation to a low value. At that point, the originators connected them in parallel. The design is highly finicky, since the exact characteristic impedance of the lines and their length determine the hub impedance values.

The revised design actually uses less space than the wheel and can also be configured circularly. We shall omit that version since the question of parallel vs. serial feeding is identical for both straight and circular triangles of dipoles. The key difference between the original wheel and the present design is that the triangle uses independent dipoles. In the arrangement shown, each exhibits a feedpoint impedance very close to 50 Ohms. Therefore, we may run 50-Ohm cables from each dipole to the hub and replicate very closely the impedance at the dipole feedpoints.

Standard treatment of the cables at the hub would
be to connect them in parallel, as suggested on the left in **Fig. 7**.
The net impedance would be from 15 to 17 Ohms, with some remnant
reactance. However, any small reactance at such low impedance values
will have a considerable impact upon any matching system that we might
try to implement. In contrast, a small reactance in series with a
higher impedance will have less impact. Therefore, we selected a series
connection system, shown in the right, ensuring that the 50-Ohm lines
to each dipole were identical. In the triangular configuration,
regardless of the feed system, the builder must ensure the same dipole
orientation to obtain the circular pattern. The modeling technique is
identical to the one applied to the triangles, except that in this
case, we form a square of very short, very thin wires, either at the
hub of the triangle or at a considerable distance from the radiating
elements.

The net impedance at the hub is about 150 Ohms,
usually with a bit of reactance. However, the reactance is rarely more
than 10% to 15% of the resistance value. Therefore, one may use a
1/4-wavelength section of cable from the series junction to the main
feedline. In this case, RG-62 93-Ohm line proved nearly ideal, with the
length adjusted to center the SWR curve in the 2-meter band. **Fig. 8**
shows the modeled (and the tested) results of the exercise.

The triangular antenna system appears only to establish that there is no practical limit to the number of identical feedlines that one may set into a serial configuration. However, when working under these simplifications, identity of line length and element structure are essential to ensure equal current at the feedpoints of the elements. Where an array requires unequal current magnitude and phase angle at each feedpoint, the modeler needs to do considerable advanced calculation, since series connections rest on voltage division.

**Conclusion**

Our goal has been to note the considerations that apply to modeling a series line assembly. Since the idea of such a method of feeding antennas is usually foreign to radio amateurs, we have provided some concrete examples that contrast parallel and series feeding methods. When an application calls for series feeding, there are ways to accomplish the modeling task for pre- and post-construction design evaluation. In most cases, adding a triangle or a square to the model will do the job.